On the decimal numbers base n

This paper focuses on the representation of a proper fraction a/b by a decimal number base n where n is any integer greater than 1. The scope is narrowed to look at only fractions where a, b are positive integers with a < b and b not equal to 0 nor equal to 1. Some relationships were found between b and n , which determine whether the representation will become either finite decimal, pure recurring decimal or mixed decimal base n . Three theorems have been proven to indicate the deciding factors and the relationships. In addition, the length of the finite decimal numbers base n was further explored.